What is Faraday's first law of electrolysis?

Faraday's first law of electrolysis states that the mass (m) of a chemical substance deposited, dissolved, or liberated at an electrode during electrolysis is directly proportional to the total electrical charge (Q = I * t) passed through the electrolyte solution: m = Z * Q = Z * I * t, where Z is the electrochemical equivalent of the substance.

What is Faraday's second law of electrolysis?

Faraday's second law of electrolysis states that when the same quantity of electric charge passes through several different electrolytes connected in series, the masses of substances deposited or liberated at the electrodes are directly proportional to their chemical equivalent weights (Equivalent Weight = Molar Mass / Valency = M / z).

What is the master formula for calculating mass deposited in electrolysis?

The unified electrolysis formula combines both of Faraday's laws: m = (M * I * t * η) / (z * F), where m is mass in grams, M is molar mass (g/mol), I is current in Amperes, t is time in seconds, η is current efficiency (fraction between 0 and 1), z is the number of electrons transferred per ion (valence), and F is Faraday's constant (96,485.33 C/mol).

How do you calculate hydrogen (H2) and oxygen (O2) gas volumes produced from water electrolysis?

In water electrolysis (2H2O -> 2H2 + O2), 2 moles of electrons produce 1 mole of H2 gas at the cathode, while 4 moles of electrons produce 1 mole of O2 gas at the anode. At standard temperature and pressure (STP: 0 °C, 1 atm), 1 mole of ideal gas occupies 22.414 L (or 24.465 L at 25 °C, 1 bar). Thus, Volume(H2) = (I * t * 22.414) / (2 * F) and Volume(O2) = Volume(H2) / 2.

How is Avogadro's number (N_A) determined experimentally using electrolysis?

Avogadro's number is experimentally determined by measuring the mass loss (Δm) of a copper or silver anode over a known time (t) and steady current (I). The total charge passed is Q = I * t, and total electrons transferred is N_e = Q / e (where e = 1.602176634 * 10^-19 C). The moles of metal dissolved is n = Δm / M, and moles of electrons is n_e = z * n. Avogadro's number is calculated as N_A = N_e / n_e = (I * t * M) / (z * Δm * e).

What is current efficiency (Faradaic efficiency) in electrolysis and why is it less than 100%?

Current efficiency (η) is the percentage ratio of actual mass or gas produced to the theoretical amount predicted by Faraday's law: η = (Actual Yield / Theoretical Yield) * 100%. In real industrial processes, efficiency is often 85% to 98% due to parasitical side reactions (such as hydrogen evolution during metal plating), ohmic electrolyte heating, and recombination of product gases.

How do you calculate required electroplating coating thickness and plating time?

To calculate electroplating time, first compute the required deposit mass: m = Surface Area * Coating Thickness * Metal Density (ρ). Then rearrange Faraday's law to solve for time: t = (m * z * F) / (M * I * η). For example, plating 10 µm of nickel on 100 cm² requires m = 100 cm² * 0.001 cm * 8.90 g/cm³ = 0.89 g, which takes 973 seconds (16.2 minutes) at 3.0 Amperes.

What is the difference between an electrolytic cell and a galvanic cell?

A galvanic (voltaic) cell converts spontaneous chemical energy into electrical energy with a positive cell potential (E_cell > 0, ΔG 0), such as electroplating, water splitting, or aluminum smelting via the Hall-Héroult process.

What role does the electrode valency (z or n) play in electrolysis calculations?

Valency (z) represents the number of moles of electrons required to reduce or oxidize one mole of ion. A higher valency requires proportionally more electric charge and time to deposit the same number of moles. For example, depositing 1 mole of Ag+ (z = 1) requires 1 Faraday (~96,485 C), while depositing 1 mole of Cu2+ (z = 2) requires 2 Faradays, and 1 mole of Al3+ (z = 3) requires 3 Faradays.

How much electrical energy (kWh) is consumed during industrial water electrolysis per kilogram of Hydrogen?

Thermodynamically, water splitting has a reversible cell potential of E_rev = 1.229 V (ΔG° = 237.2 kJ/mol H2) and a thermoneutral voltage of E_th = 1.481 V (ΔH° = 285.8 kJ/mol). In practice, commercial PEM and alkaline electrolyzers operate at 1.8 V to 2.2 V to overcome kinetic overpotentials, consuming approximately 50 to 55 kWh of electricity per kilogram of green hydrogen produced (39.4 kWh/kg theoretical Higher Heating Value).

Faraday's Laws & Electrochemistry Suite • 100% Free

Electrolysis Calculator

Calculate mass deposited ($m = \frac{M \cdot I \cdot t \cdot \eta}{z \cdot F}$), water splitting gas volumes ($\text{H}_2/\text{O}_2$), electroplating layer thickness ($\mu\text{m}$), and Avogadro's number ($N_A$) from Faraday's laws.

Benchmark Electrolysis & Electroplating Presets 1-Click to auto-populate electrochemical parameters

Faraday Electrolysis Parameters

m = MIt/zF

Calculate Variable:

Electroactive Substance / Ion: M = 63.546 g/mol, z = 2

Electric Current ($I$):

Electrolysis Duration ($t$):

Current Efficiency ($\eta$): 100.0%

Electrochemical Yield & Stoichiometry Faraday Law 100% Efficient

Mass of Substance Deposited ($m$):

11.853 g

0.1865 moles • 11,853 mg

Total Electric Charge Passed ($Q$):

36,000 C

0.3731 Faradays (mol e⁻)

Electrochemical Equiv (Z) 0.3293 mg/C

Moles of Electrons 0.3731 mol e⁻

Equivalent Weight 31.773 g/eq

Number of Electrons

2.247 × 10²³

$N_e = Q / e$

Deposit Volume

1.323 cm³

$V = m / \rho$

Current Density

N/A

$j = I / A$

Electrochemical Reaction Summary & Faraday Law Cathode Reduction

Passing a current of 5.00 A for 2.00 hours transfers a total of 36,000 Coulombs (0.3731 Faradays). For Copper reduction ($\text{Cu}^{2+} + 2e^- \to \text{Cu}$), each mole of copper requires 2 moles of electrons ($z=2$), yielding 11.853 grams (0.1865 moles) of pure metallic copper deposited at the cathode.

Physical Principles & Mathematical Derivation of Faraday's Laws

In 1834, Michael Faraday published his quantitative laws of electrochemistry, establishing the fundamental relationship between electric charge, chemical stoichiometry, and mass transport across electrode-electrolyte interfaces:

1. Faraday's First Law of Electrolysis

The mass ($m$) of a chemical substance deposited or liberated at an electrode is directly proportional to the quantity of electricity ($Q = I \cdot t$) passed through the electrolyte:

$$m = Z \cdot Q = Z \cdot I \cdot t$$

where $Z$ is the electrochemical equivalent (mass deposited per Coulomb of charge, in $\text{g/C}$ or $\text{mg/C}$).

2. Faraday's Second Law & Master Formula

For a given electric charge, the mass deposited is proportional to the substance's chemical equivalent weight ($E_w = M/z$). Combining both laws yields the universal master equation:

$$m = \frac{M \cdot I \cdot t \cdot \eta}{z \cdot F}$$

where $F = 96,485.33212\,\text{C/mol}$ is Faraday's constant and $\eta$ is Faradaic current efficiency.

Electrochemical Equivalent ($Z$) & Density Reference Matrix

Standard Electrode Constants

Key electrochemical data for common industrial metals and gases, where $Z = \frac{M}{z \cdot F}$:

Element / Ion	Half-Reaction	Valency ($z$)	Molar Mass ($M$)	$Z$ (mg/C)	Density ($\text{g/cm}^3$)
Silver ($\text{Ag}^+$)	$\text{Ag}^+ + e^- \to \text{Ag}$	1	107.868 g/mol	1.1180 mg/C	10.49
Copper ($\text{Cu}^{2+}$)	$\text{Cu}^{2+} + 2e^- \to \text{Cu}$	2	63.546 g/mol	0.3293 mg/C	8.96
Gold ($\text{Au}^{3+}$)	$\text{Au}^{3+} + 3e^- \to \text{Au}$	3	196.967 g/mol	0.6805 mg/C	19.32
Nickel ($\text{Ni}^{2+}$)	$\text{Ni}^{2+} + 2e^- \to \text{Ni}$	2	58.693 g/mol	0.3041 mg/C	8.90
Zinc ($\text{Zn}^{2+}$)	$\text{Zn}^{2+} + 2e^- \to \text{Zn}$	2	65.380 g/mol	0.3388 mg/C	7.14
Aluminum ($\text{Al}^{3+}$)	$\text{Al}^{3+} + 3e^- \to \text{Al}$	3	26.982 g/mol	0.0932 mg/C	2.70
Hydrogen ($\text{H}_2$)	$2\text{H}^+ + 2e^- \to \text{H}_2$	2	2.016 g/mol	0.0104 mg/C	0.0899 g/L (STP)

Thermodynamics of Water Splitting: Green Hydrogen & Energy Metrics

Water electrolysis produces high-purity hydrogen at the cathode and oxygen at the anode via the endothermic reaction:

$$2\text{H}_2\text{O}(l) \longrightarrow 2\text{H}_2(g) + \text{O}_2(g) \quad (\Delta G^\circ = +237.2\,\text{kJ/mol}, \Delta H^\circ = +285.8\,\text{kJ/mol})$$

1. Reversible Voltage ($E_{\text{rev}}$)

The minimum thermodynamic potential required at 25 °C and 1 bar:

$$E_{\text{rev}} = \frac{\Delta G^\circ}{nF} = \frac{237,200}{2 \times 96485} = \mathbf{1.229\,\text{V}}$$

2. Thermoneutral Voltage ($E_{\text{th}}$)

Voltage where heat absorbed matches enthalpy without external heating:

$$E_{\text{th}} = \frac{\Delta H^\circ}{nF} = \frac{285,800}{2 \times 96485} = \mathbf{1.481\,\text{V}}$$

3. Specific Energy Consumption

Commercial electrolyzers (PEM, Alkaline) operate at $1.8 - 2.2\,\text{V}$ due to overpotentials:

$$\text{Consumption} \approx \mathbf{50 - 55\,\text{kWh/kg } H_2}$$

Determining Avogadro's Number ($N_A$) Using Electrolysis

Avogadro's constant ($N_A = 6.02214076 \times 10^{23}\,\text{mol}^{-1}$) can be precisely determined in the laboratory using copper electrolysis:

1. Pass a constant electric current $I$ through a $\text{CuSO}_4$ electrolytic cell for time $t$, causing the copper anode to dissolve: $\text{Cu}(s) \to \text{Cu}^{2+}(aq) + 2e^-$.

2. Measure the exact mass loss of the anode ($\Delta m$). The moles of copper dissolved is $n_{\text{Cu}} = \frac{\Delta m}{M_{\text{Cu}}}$, requiring $n_e = 2 \times n_{\text{Cu}}$ moles of electrons.

3. The total number of electrons passed is $N_e = \frac{Q}{e} = \frac{I \cdot t}{e}$ (where $e = 1.602176634 \times 10^{-19}\,\text{C}$).

$$N_A = \frac{N_e}{n_e} = \frac{I \cdot t \cdot M_{\text{Cu}}}{2 \cdot \Delta m \cdot e}$$

Step-by-Step Worked Case Studies: Refining, Galvanizing & Avogadro Lab

Case 1: Copper Refining Faraday Law

Given: $I = 5.0\,\text{A}$, $t = 2.0\,\text{h} = 7200\,\text{s}$, $\text{Cu}^{2+}$ ($M = 63.546\,\text{g/mol}, z = 2$):

$Q = 5.0 \times 7200 = 36,000\,\text{C}$
$m = \frac{63.546 \times 36000}{2 \times 96485.33} = \mathbf{11.853\,\text{g}}$
Moles $= \frac{11.853}{63.546} = \mathbf{0.1865\,\text{mol}}$

Case 2: Zinc Galvanizing Electroplating

Given: Area $= 200\,\text{cm}^2$, thickness $= 15\,\mu\text{m} = 0.0015\,\text{cm}$, $\rho = 7.14\,\text{g/cm}^3$, $I = 5\,\text{A}$:

$m = 200 \times 0.0015 \times 7.14 = \mathbf{2.142\,\text{g}}$
$t = \frac{2.142 \times 2 \times 96485.33}{65.38 \times 5.0} = 1264\,\text{s}$
Duration $= \mathbf{21.07\,\text{minutes}}$

Case 3: Avogadro's Number Experimental

Given: $I = 0.50\,\text{A}$, $t = 1800\,\text{s}$, $\Delta m_{\text{Cu}} = 0.2965\,\text{g}$:

$Q = 0.50 \times 1800 = 900\,\text{C}$
$N_A = \frac{900 \times 63.546}{2 \times 0.2965 \times 1.6022 \times 10^{-19}}$
$N_A = \mathbf{6.028 \times 10^{23}\,\text{mol}^{-1}}$ ($0.10\%$ error)

Frequently Asked Questions (FAQ)

Authoritative answers to common questions about calculating electrolysis mass, plating time, gas volumes, and Avogadro's number.

Electrolysis Calculator

Faraday Electrolysis Parameters

Water Splitting Reactor Specs

Electroplating Geometry

Avogadro Lab Data

Physical Principles & Mathematical Derivation of Faraday's Laws

Electrochemical Equivalent (\(Z\)) & Density Reference Matrix

Thermodynamics of Water Splitting: Green Hydrogen & Energy Metrics

Determining Avogadro's Number (\(N_A\)) Using Electrolysis

Step-by-Step Worked Case Studies: Refining, Galvanizing & Avogadro Lab

Frequently Asked Questions (FAQ)

Element / Ion	Half-Reaction	Valency (\(z\))	Molar Mass (\(M\))	\(Z\) (mg/C)	Density (\(\text{g/cm}^3\))
Silver (\(\text{Ag}^+\))	\(\text{Ag}^+ + e^- \to \text{Ag}\)	1	107.868 g/mol	1.1180 mg/C	10.49
Copper (\(\text{Cu}^{2+}\))	\(\text{Cu}^{2+} + 2e^- \to \text{Cu}\)	2	63.546 g/mol	0.3293 mg/C	8.96
Gold (\(\text{Au}^{3+}\))	\(\text{Au}^{3+} + 3e^- \to \text{Au}\)	3	196.967 g/mol	0.6805 mg/C	19.32
Nickel (\(\text{Ni}^{2+}\))	\(\text{Ni}^{2+} + 2e^- \to \text{Ni}\)	2	58.693 g/mol	0.3041 mg/C	8.90
Zinc (\(\text{Zn}^{2+}\))	\(\text{Zn}^{2+} + 2e^- \to \text{Zn}\)	2	65.380 g/mol	0.3388 mg/C	7.14
Aluminum (\(\text{Al}^{3+}\))	\(\text{Al}^{3+} + 3e^- \to \text{Al}\)	3	26.982 g/mol	0.0932 mg/C	2.70
Hydrogen (\(\text{H}_2\))	\(2\text{H}^+ + 2e^- \to \text{H}_2\)	2	2.016 g/mol	0.0104 mg/C	0.0899 g/L (STP)